Modify PATH

You could modify PATH to move /Users/me/miniconda2/bin after /usr/local/bin or remove it from PATH completely. The downside is that if you rely on other binaries in ~/miniconda2/bin they will no longer be found when executing them by name.

Move R out of the way

Another option would be to move ~/miniconda/bin/R out of the way, for example using

mv ~/miniconda/bin/R ~/miniconda/bin/R-miniconda

Afterwards R will be run from the next location in $PATH, but if you update miniconda2 it may return.

Link to R further up in the PATH (easiest/best)

Finally, you could make sure that there is an R executable in something that is further up the $PATH. This is probably the easiest and most effective option.

First, make sure you have a bin folder in your home directory. If this is not the case, create it and then restart the terminal. The restart should cause the code in ~/.profile to add that folder to your $PATH. You can verify by doing echo $PATH. In the above example the path already contains /Users/me/bin at the very top.

Next, create a soft link to the R binary in the newly created folder:

ln -s /usr/local/bin/R ~/bin/R

You should now be able to execute R, which will prefer the softlink created, which will execute the one you like. If it does not work right away execute hash -r or restart the terminal.

Email codedump link for Running newer version of R from terminal when older version is invoked by default